| id | imps79 | imps79b | imps79o | tx | week |
|---|---|---|---|---|---|
| 1103 | 5.5 | 1 | 4 | 1 | 0 |
| 1103 | 3.0 | 0 | 2 | 1 | 1 |
| 1103 | 2.5 | 0 | 2 | 1 | 3 |
| 1103 | 4.0 | 1 | 2 | 1 | 6 |
| 1104 | 6.0 | 1 | 4 | 1 | 0 |
| 1104 | 3.0 | 0 | 2 | 1 | 1 |
| 1104 | 1.5 | 0 | 1 | 1 | 3 |
| 1104 | 2.5 | 0 | 2 | 1 | 6 |
| 1105 | 4.0 | 1 | 2 | 1 | 0 |
| 1105 | 3.0 | 0 | 2 | 1 | 1 |
| 1105 | 1.0 | 0 | 1 | 1 | 3 |
| 1105 | NA | NA | NA | 1 | 6 |
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
\[\mathbf{Y}_{ij} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{\gamma} + \boldsymbol{\epsilon}\]
id: ID variableimps79: Continuous measure of schizophrenia (1 to 7)imps79b: Binary measure of schizophrenia (3.5+)imps79o: Ordinal measure of schizophrenia (Cuts: 2.5+, 4.5+, 5.5+)tx: Placebo (0) or treatment (1)week: Week of study (0, 1, 3, 6)| id | imps79 | imps79b | imps79o | tx | week |
|---|---|---|---|---|---|
| 1103 | 5.5 | 1 | 4 | 1 | 0 |
| 1103 | 3.0 | 0 | 2 | 1 | 1 |
| 1103 | 2.5 | 0 | 2 | 1 | 3 |
| 1103 | 4.0 | 1 | 2 | 1 | 6 |
| 1104 | 6.0 | 1 | 4 | 1 | 0 |
| 1104 | 3.0 | 0 | 2 | 1 | 1 |
| 1104 | 1.5 | 0 | 1 | 1 | 3 |
| 1104 | 2.5 | 0 | 2 | 1 | 6 |
| 1105 | 4.0 | 1 | 2 | 1 | 0 |
| 1105 | 3.0 | 0 | 2 | 1 | 1 |
| 1105 | 1.0 | 0 | 1 | 1 | 3 |
| 1105 | NA | NA | NA | 1 | 6 |
| week | mean_c | mean_b | N |
|---|---|---|---|
| 0 | 5.367 | 0.986 | 434 |
| 1 | 4.571 | 0.843 | 426 |
| 3 | 4.020 | 0.711 | 374 |
| 6 | 3.310 | 0.484 | 335 |
\[\eta = \mathbf{X}\boldsymbol{\beta}\]
week as a predictor of imps79bweek: 0, 1, 3, 6imps79b: 0 (less than 3.5 on imps79), 1 (3.5+ on imps79)tx)
Call:
geeglm(formula = imps79b ~ 1 + week, family = binomial("logit"),
data = schizx1, id = schizx1$id, corstr = "unstructured")
Coefficients:
Estimate Std.err Wald Pr(>|W|)
(Intercept) 2.59459 0.11876 477.3 <0.0000000000000002 ***
week -0.45017 0.02767 264.7 <0.0000000000000002 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation structure = unstructured
Estimated Scale Parameters:
Estimate Std.err
(Intercept) 0.9646 0.1007
Link = identity
Estimated Correlation Parameters:
Estimate Std.err
alpha.1:2 0.05390 0.05343
alpha.1:3 -0.02855 0.03265
alpha.1:4 -0.01890 0.03342
alpha.2:3 0.56341 0.10114
alpha.2:4 0.15242 0.06617
alpha.3:4 0.51550 0.07964
Number of clusters: 437 Maximum cluster size: 4
\[ln\left(\frac{\hat{p}}{1-\hat{p}}\right) = b_0 + b_1 (week)\]
| tx | week0 | week1 | week3 | week6 |
|---|---|---|---|---|
| 0 | 0.972 | 0.880 | 0.713 | 0.463 |
| 1 | 0.982 | 0.802 | 0.574 | 0.340 |
\[\eta = \mathbf{X}\boldsymbol{\beta}\]
week as a predictor of imps79bweek: 0, 1, 3, 6imps79b: 0 (less than 3.5 on imps79), 1 (3.5+ on imps79)tx) in classGeneralized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula: imps79b ~ 1 + week + (1 + week | id)
Data: schizx1
AIC BIC logLik deviance df.resid
1291.6 1318.4 -640.8 1281.6 1564
Scaled residuals:
Min 1Q Median 3Q Max
-2.8446 0.0898 0.1139 0.2646 1.0822
Random effects:
Groups Name Variance Std.Dev. Corr
id (Intercept) 4.413 2.101
week 0.711 0.843 -0.13
Number of obs: 1569, groups: id, 437
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.386 0.539 8.14 0.00000000000000041 ***
week -0.793 0.118 -6.71 0.00000000001954283 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
week -0.817
\[ln\left(\frac{\hat{p}}{1-\hat{p}}\right) = b_0 + b_1 (week)\]
week, tx, and their product